"从事间谍活动的" can be translated into English as "engaged in espionage activities" or "involved in spy work".
For example:
He was found to be engaged in espionage activities. （他被发现从事间谍活动。）
The suspect was accused of being involved in spy work for a foreign power. （这名嫌疑人被指控为外国势力从事间谍工作。）